Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles.
Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles.
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DOI：
10.1103/physrevlett.119.028003
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发表时间：
2016-11
影响因子：
8.6
通讯作者：
A. Baule
中科院分区：
文献类型：
--
作者：
A. Baule
特定形状的颗粒的随机顺序吸附（RSA）被用于各种各样的环境中来模拟颗粒聚集和堵塞。这些模型的一个关键特征是观测到的渐近干扰覆盖范围Δ t^{-ν}随t→∞的代数时间依赖性。然而，除了最简单的单分散球体吸附在一条线上的RSA（雷尼开创性的“停车问题”）之外，指数ν的确切值是未知的，其中ν=1可以通过分析推导出来。经验模拟研究已经在逐个案例的基础上证明，对于一般的非球形粒子，ν=1/（d+d[over λ]），其中d表示域的维数，d[over λ]表示粒子的取向自由度的数量。在这里，我们解决了这个长期存在的问题，分析d=1的情况下，“巴黎停车问题。“我们证明，特别是，标度指数取决于颗粒形状，与原来的猜想相反，值得注意的是，福尔斯分为两个普适性类：（i）对于具有光滑接触距离的形状，v =1/（1+d[over λ]/2），例如，椭圆体，以及（ii）对于具有奇异接触距离的形状，v =1/（1+d[over λ]），例如，球柱体和多面体。精确解特别解释了为什么许多经验观察到的标度落在这两个极限之间。
Random sequential adsorption (RSA) of particles of a particular shape is used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the observed algebraic time dependence of the asymptotic jamming coverage ∼t^{-ν} as t→∞. However, the exact value of the exponent ν is not known apart from the simplest case of the RSA of monodisperse spheres adsorbed on a line (Renyi's seminal "car parking problem"), where ν=1 can be derived analytically. Empirical simulation studies have conjectured on a case-by-case basis that for general nonspherical particles, ν=1/(d+d[over ˜]), where d denotes the dimension of the domain, and d[over ˜] the number of orientational degrees of freedom of a particle. Here, we solve this long-standing problem analytically for the d=1 case-the "Paris car parking problem." We prove, in particular, that the scaling exponent depends on the particle shape, contrary to the original conjecture and, remarkably, falls into two universality classes: (i) ν=1/(1+d[over ˜]/2) for shapes with a smooth contact distance, e.g., ellipsoids, and (ii) ν=1/(1+d[over ˜]) for shapes with a singular contact distance, e.g., spherocylinders and polyhedra. The exact solution explains, in particular, why many empirically observed scalings fall in between these two limits.